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ASTRONOMY 



BY 



HAROLD JACOBY 

BUTHERFURD PROFESSOR OF ASTRONOMY 
COLUMBIA UNIVERSITY 



THE COLUMBIA UNIVERSITY PRESS 
1908 



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ASTRONOMY 



A LECTURE DELIVERED AT COLUMBIA UNIVERSITY 

IN THE SERIES ON SCIENCE, PHILOSOPHY AND ART 

NOVEMBER 6, 1907 




ASTRONOMY 



BY 



HAROLD JACOBY 

RUTHERFURD PROFESSOR OF ASTRONOMY 
COLUMBIA UNIVERSITY 



THE COLUMBIA UNIVERSITY PRESS 
1908 



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TuBftARY of OOt^SRlS 
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FEB "10 1^08 
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Copyright, 1908, 
By THE COLUMBIA UNIVERSITY PRESS. 



Set up, and published January, 1908. 



ASTRONOMY 



The present condition of astronomic science is a subject 
too extended to be brought easily within the limits suitable 
to this occasion; and yet it seems to me pertinent to begin 
with a seeming prolixity, to make an attempt at answering 
the question : Why is it desirable to carry on astronomic re- 
searches at all? I shall even take the liberty of entering 
upon this point with some particularity because I desire a 
test by means of which it may be possible to distinguish be- 
tween genuine, and therefore desirable researches, and 
those undertaken mistakenly, through ignorance of any 
such test, or, worse still, for the mere exploitation of per- 
sonal reputation and to satisfy the fetish-worship of printed 
publication. 

Perhaps the most important element to consider in form- 
ing a judgment of any man's performance is motive. 
You may commit an act of forgery : it will go unpunished 
by the law unless a criminal motive can be proved. So I 
may undertake astronomic researches; I may fail totally; 
but my efforts will have been justified if my motive was 
the right one. 

Now what is this motive which thus seems to me one es- 
sential pre-requisite to genuine research? In a word, it is 
the same as the motive of the artist. Consciously or uncon- 
sciously, the true astronomer strives ever to create a work 
of art. But what is art, a great painting, sculpture, music, 
or a monument of architecture ? In the last analysis a great 
painting is but a smeared canvas, sculpture is a chipped 

5 



stone, music is a collection of noise, and a monument of 
architecture is a shelter from the weather. But they are 
something more than this. He who created them labored 
and suffered that two or three perhaps in each succeeding 
generation might take from them that exquisitely subtle 
emotion that is for him alone who can feel art. The true 
test of art is its power to give the purest and the noblest 
pleasure that the mind of man can derive from the work of 
man ; to give this pleasure to the cognoscenti, however few. 
The ecstasy of the musician, brought about by great music, 
is identical with the emotion of the mathematician when he 
studies the works of the masters. If this be true, and it is 
true, then is mathematics the most sublime of all the 
arts in that it appeals to the intellect directly; the other 
arts, like music, require the grosser senses through which to 
exert their influence. Only, now and again, some rare 
spirit, such as that which dwelt within the frame of deaf 
Beethoven, can joy in soundless melodies that breathe amid 
the crabbed characters of written music, as kindred mel- 
odies breaihe among the dead equations of astronomy. 
Therefore I think that researches in science will be written 
down in the temple of fame if they are inscribed also in 
the temple of art, and not otherwise. 

It is surely impossible to justify these pursuits on any 
other grounds. The much vaunted search for truth, for the 
sake of truth, — this, so far as it is other than a manifesta- 
tion of conscious or unconscious effort to create art, so far 
is it but an impertinent curiosity to pry into things concealed 
by nature. Nor can we accept utilitarian value as a sufficient 
justification. Now I yield to no man in my appreciation of 
purely utilitarian motives and purely utilitarian results. 
This I propose to emphasize by describing briefly some of 
the more important practical applications of astronomy. 
For my science, more perhaps than any other of the more 
abstruse sciences, enters most directly, most intimately and 

6 



most frequently into the daily life of the people at large. 
There are at least three practical things that astronomy 
does for us; and without these modern civilization and 
modern life would be impossible. The first is the regula- 
tion of time. Few persons stop to think how this is done 
to-day. When we desire to set our watches or clocks aright 
we simply compare them with an accurate timepiece called 
a regulator such as may be found in every jeweler's shop. 
But how does the jeweler regulate his regulator? In every 
city there is a network of telegraph circuits. One of these 
is called the "time-wire." For a moderate annual compen- 
sation, the telegraph company will run a loop from the 
time-wire circuit into any building. A telegraphic sounder 
is attached to this loop, and thus the beats of a standard 
clock placed in the central office of the telegraph company 
can be repeated by the sounder for comparison with the 
jeweler's regulator. By a simple system of omitting one 
beat before the beginning of each minute, and a different 
number of beats before the beginning of the hour, it be- 
comes possible to adjust the minute and hour hands of the 
jeweler's regulator as well as the second hand into accord 
with the company's standard. 

But this simply transfers our problem from the jeweler's 
regulator to the company's standard, and would be of no 
use so far as accuracy is concerned, if we had no means of 
correcting errors in the running of the standard itself. Of 
course this clock is always made very carefully, and no ex- 
pense is spared in assuring the greatest precision in all its 
mechanical parts, so far as precision can be attained by the 
work of human hands. In spite of all precautions, how- 
ever, slight errors will occur, and these may accumulate 
into quantities of quite considerable magnitude as time 
goes on. To correct them, we must have recourse to a na- 
tural standard of time, we must appeal to the stars them- 
selves, and here we need the astronomer. 

7 



It is unnecessary at this point to enter into any detailed 
explanation of how he performs his part of the work. It 
will suffice to point out that the instruments mounted in 
any modern permanent observatory enable him to deter- 
mine the error of his clock within a very few hundredths of 
a second by an hour's observations on any clear night. A 
telegraphic comparison with the company's standard then 
transfers this accurate determination of clock error to the 
latter instrument, from which it is in turn distributed to the 
jewelers' regulators, tod from them to the people at large. 
This work is important, essential even ; but it requires one 
astronomer only, very little of his time, is purely routine in 
character, and cannot be called research in the full sense of 
the word. 

The second definite function of astronomy in practical 
affairs has to do with navigation. The sure and certain 
guiding of a ship across the trackless, unmarked ocean is 
one of the many things startling, even mysterious to the 
layman, though simple enough to those conversant with 
the underlying astronomical principles. You will remem- 
ber that the navigator determines the position of his ship 
day after day by observations with an astronomical instru- 
ment called a sextant. But these observations alone would 
be of little value. They are but the raw material, and 
must be subjected to a refining process called "reduction" 
or computation before they will furnish the information de- 
sired. To carry out this process of computation the navi- 
gator needs certain printed astronomical tables, that give 
him the positions of the sun, moon and other heavenly 
bodies on the sky for every day in the year. 

These tables are published by the various civilized gov- 
ernments of the world, and are called Nautical Almanacs. 
In their preparation we need again the services of one 
skilled astronomer, to superintend the work, and to assist 
him a corps of more or less mechanical assistants and clerks. 

8 



Like the regulation of time, this work is indispensable, but 
it is again almost altogether an affair of routine at the 
present day, and does not partake of the nature of genuine 
research. 

The third practical use of my science to which I shall 
venture to call your attention has to do with the prepara- 
tion of maps and charts. The ordinary processes of the sur- 
veyor need but to be strengthened by increased power of 
instruments and increased precision of observation to make 
them applicable to charting larger portions of the earth's 
surface, such as an entire continent or the coast lines of a 
great country. But when such maps and charts have been 
thus completed, they furnish merely a correct picture of 
the earth's surface, — showing towns, rivers, bays and capes 
in their proper relative positions. In this form they are 
not of any great practical use. To perfect them, it is 
necessary to mark upon them the latitude and longitude 
lines, and these cannot be placed correctly without the aid 
of astronomical observations. The latitudes and longitudes 
of a number of points covered by the survey must be deter- 
mined astronomically, and then the proper reference lines 
can be inscribed on the charts to complete them. I must 
here once more refrain from a detailed description of mod- 
ern methods used in this process: it is sufficient to point 
out that these things too are entirely routine in their char- 
acter. However important to commercial civilization, they 
are outside the pale, and seldom come within my notion 
of what constitutes true research. 

This much I have said to show how high an appreciation 
I have for purely utilitarian motives and purely utilitarian 
results. Utilitarian motives are not inferior to research; 
they are not superior to research ; they are not equal to re- 
search ; they are simply other than research. 

And now permit me to illustrate my idea still further by 
describing briefly a modern research that seems to me gen- 

9 



uine, absolutely. I select for this purpose a piece of work 
by Gauss, he who was called, rightly, by those of his con- 
temporaries who were wont to follow the good old custom 
of writing in the Latin language: Gauss, clarissimus; 
Gauss, celeberrimus ; and, finally, Gauss, incompara- 
bilis. 

It was on the very first day of the nineteenth century 
that Piazzi of Palermo discovered the minor planet Ceres, 
the first to be added to the seven previously well known. 
Illness prevented Piazzi from observing the new object 
during more than six weeks ; and as news of planetary dis- 
covery traveled slowly in those days, it was not until .the 
latter part of March that astronomers in northern Europe 
heard of the new object. By that time Ceres had passed 
so near the sun that it could not be observed, and great ex- 
citement resulted from the fear that it would never again 
be found, because astronomers would not, know exactly 
where to look for it when the time should again come to 
attempt observation. 

And there was good reason for this fear. The older 
planets had of course been observed throughout many or- 
bital revolutions, and it was a difficult, unsolved problem 
to determine the path of such a moving body when the 
available observations extended through a very small frac- 
tion only of the planet's total circuit around the sun. With- 
out a satisfactory solution of the problem, a further search 
would be well-nigh hopeless when it should again become 
possible to undertake one. Gauss was then a young man 
of twenty-three at Gottingen. He attacked the difficulty, 
overcame it, and his computations made the re-discovery of 
Ceres easy in the following December. He had produced 
his deathless work on the theory of motion, but he spent 
eight long years perfecting it before he gave it to the press. 
When it appeared, the world possessed one more true work 
of art. Fallible and imperfect must ever be the results of 

10 



human effort. No one can reach his ideal. But the The- 
oria Motus stands immaculate, unapproachable, such as 
might be a marble of Phidias ; none have since added any- 
thing to it. This is in truth a hall-mark of art, that the 
thing itself shall approximate perfection, shall be the ut- 
most effort of the utmost man. 

And now let me contrast with this another modern re- 
search that seems to illustrate the kind of scientific work 
sometimes undertaken in ignorance of the true test of value. 
I refer to the canals of Mars. By no conceivable possibil- 
ity can this work convey to any one an impression of life 
everlasting. About it all is an air of unreality; one feels 
almost as if mankind would forget it before actually be- 
coming aware of its existence. The strongest argument in 
favor of Martian canals is the intense desire of certain hu- 
man beings to know other planets inhabited. 

If I may be permitted to do so, I should like to turn aside 
here for a moment, and inquire what we mean by seeing a 
thing. What is the actual process? Light waves coming 
from the object under examination travel through the 
luminif erous ether, and firfally impinge upon the outer sur- 
face of the eye, like surf breaking on an ocean shore. They 
are concentrated or brought to a focus by the lens in our eye, 
and produce some kind of an effect which we do not quite 
understand upon the rods and cones of the retina. This 
results in an impression being received by the brain, via the 
optic nerve. The brain in its turn does an unexplained 
something with this impression; what we think we see is 
equal to that which came through the eye and optic nerve 
plus what the brain does to it on its arrival at headquarters. 
It is this little plus, I fear, that has helped to create the 
Martian canals and especially the intelligent engineers who 
built them. The human brain cannot distinguish between 
that which comes through the optic nerve, and that which 
the brain adds to it. The sum is what we seem to see. 

1.0FC. ^^ 



Once started on the downward path of discovery, the 
rest is easy. We see what we desire and hope to see; do 
what we will we cannot prevent this ; as Shakespeare says : 
"Increase of appetite had grown by what it fed on." 

Again, people are very apt to think they see what they 
are told by others is to be seen. Not many years ago a 
shipful of astronomical tourists was sent out from this 
country to one of the Norway fjords, where an eclipse of 
the sun was to occur. An unfortunate astronomical lec- 
turer accompanied the expedition charged with the duty of 
delivering two addresses to the ship's company. One of 
these was to precede the eclipse, to tell the people what they 
were about to see ; the other was to follow the phenomenon, 
to tell them what they had seen. This seems an admirable 
arrangement, probably devised by some one who knew well 
the psychology of the matter. 

If the substratum of observed facts is abandoned,— and 
I think most of it will be abandoned when we come to com- 
pare impartially the drawings and photographs made by 
various observers, — it becomes useless to point out contra- 
dictions and improbabilities in the dream-fabric of theory 
built upon it. I can summarize for you several bookfuls 
of Martian knowledge very briefly thus: certain observers 
think they see some rather hazy markings on the planet. 
That is all there is to it. 

And now permit me to devote the few minutes of your 
time still remaining at my disposal to one or two of the 
more important problems now pending before astronomers. 
I shall avail myself to a limited extent of Forster's ad- 
mirable division of the subject into three parts, astro- 
mechanics, astrometry, and astrophysics. The first of 
these deals with the mechanical laws of motion based on the 
theory of gravitation, the precession of the equinoxes, the 
nutation of the earth's axis, planetary perturbations, etc. 
The second has to do rather with the actual measurement 

12 



of objects in the heavens, their sizes and relative positions 
on the sky. The third studies the physical nature of celes- 
tial bodies and determines the chemical elements of which 
they consist. 

As before, the stern necessity for brevity compels me to 
limit myself strictly to the most important part of my sub- 
ject: I therefore select astro-mechanics, and under that 
head cannot do better than call your attention to the pres- 
ent attitude of astronomers toward the law of gravitation 
itself. This law declares that every particle of matter in 
the universe attracts every other particle of matter. The 
precise conditions under which such attraction is supposed 
to have effect I disregard for the moment as a matter of 
detail. But is there really such a thing as gravitation? 
Has this law a real physical existence, and does it actually 
hold sway in our world? In the first place, the law itself is 
contrary to ordinary ideas of common sense. How can any 
particle of matter pull any other particle, when there is no 
connecting link through which the pull can be exerted? 
This objection we may pass over because we can accept the 
law even though we are unable to understand just how or 
why it exists and acts. The question is, to what extent does 
it enable us to explain for the past and predict for the 
future all those intricate convolutions of motive that we ob- 
serve among the planetary bodies in our solar system and 
even among the distant congeries of stars. 

It is a singular fact that all these motions can be thus 
explained for the past and predicted for the future without 
using the law of gravitation, yet with an accuracy as great 
as this law itself renders possible. Existing tables of plan- 
etary and lunar motion have been computed by the aid of 
certain formulas obtained from the law of gravitation by 
means of mathematical analysis. These formulas consist 
of a long series of parts or "terms" which must be com- 
puted separately and the results added in order to find the 
L OF C. 13 



planet's position on the sky to be printed in the nautical 
almanacs to which I have already made reference and sub- 
sequently compared with actual observation for a verifica- 
tion of theoretical law. 

Now all these terms are what mathematicians call peri- 
odic in form. This means that while any given term may 
increase as time goes on, such increase cannot continue 
without limit. There must come an epoch when it will 
again begin to decrease, and so on alternately to the end of 
time. It was on this peculiarity of periodicity that Laplace 
based his famous but not quite rigorous mathematical dem- 
onstration of stability in our solar system. All terms in all 
motions being strictly periodic, it follows that all changes 
in the system are likewise periodic. No matter how intri- 
cate may be the changes occurring in the system, these 
cannot continue indefinitely, and everything must return 
again to its original form and condition after the lapse of 
sufficient ages of time. 

But the very fact of uniform periodicity in these terms 
l)rings out a most curious circumstance. The ancient 
Ptolemaic theory of the universe was periodic too. Ptolemy 
made the earth immobile, and all orbits were circular. The 
revolving planet did not travel in the original circle, but 
upon the circumference of a second smaller circle, perhaps, 
whose centre moved in the original curve. Now if we 
apply modern mathematical methods to Ptolemy's theory 
of the universe, it is possible to show that we can thus re- 
produce all Laplace's periodic terms by simply postulating 
a sufficient number of these circles moving one upon the 
other. For each term in Laplace's series we must have one 
more Ptolemaic circle. This having been done, the actual 
formulas to be used in the computation of a planet's place 
in the sky become identical, whether we deduce them by the 
methods of Newton and Laplace or from the principle of 
Ptolemy. Consequently, the agreement between theory 

14 



and observation is the same either way ; and such agreement 
fails as a test to determine whether Ptolemy or Newton 
had a correct theory of the universe. The one thing that 
leads us to accept Newton's law of gravitation is that 
this law is extremely simple compared with those intrica- 
cies of endless eccentric circles. And the human mind 
chooses to assume that the universe is constructed on a 
simple plan rather than an extremely complicated one. 
Thus gravitation rests ultimately to some extent on a mere 
peculiarity of the human mind. 

Now I have no desire to be made, to-night, the subject of 
an Associated Press dispatch, in which I shall be heralded 
throughout this land as having abandoned the law of gravi- 
tation, and returned to the old Ptolemaic theory of the uni- 
verse. I therefore state explicitly that such is not the case. 
I have merely called attention to the above interesting 
facts, in order that I may mention what is the last word of 
science on this matter. We cannot do better than seek it 
in Simon Newcomb's 1895 memoir entitled "The elements 
of the four inner planets and the fundamental constants of 
astronomy." 

Newton, as you know, postulated that the attraction of 
gravity diminishes proportionately with the square of the 
distance. If a body pulls another with a certain strength 
at a certain distance, then this pull will be diminished to 
one-fourth its former force if the distance between the 
bodies be doubled. Now there exist certain outstanding 
discrepancies between observed and computed motions 
which have never been explained satisfactorily. This does 
not necessarily prove that the law of gravitation is non- 
existent, because the failure in explanation may be due 
simply to the feebleness of man's mathematical powers. 
Something may have been overlooked somewhere in the 
endless and seemingly inextricable complexities of mathe- 
matical deductions. But this is improbable too; for you 

15 



may well imagine that no stone has been left miturned by 
successive generations of able investigators. 

For this reason it has been proposed to alter the law of 
gravitation slightly, so as to explain these little theoretical 
discrepancies. The proposition is to suppose the attraction 
to diminish, not as the square of the distance, but in a man- 
ner differing very slightly from the square. This I may 
call the law of modified gravitation. To Newcomb the 
hypothesis seems "provisionally not inadmissible," and 
more unobjectionable than others that have been proposed. 
But in abandoning the Newtonian form of the law we lose 
its simplicity ; which, as I have said, seems to be the strong- 
est argument for its reality. 

In the light of Newcomb's dicta, we must to-day charac- 
terize Newton's law as a working hypothesis merely, and 
one that even as such is open to some doubt. I can tell you 
nothing that more strongly emphasizes the mutable and 
perishable character of results attained by the human intel- 
lect nor anything that better illustrates the ideas with which 
I began my address. But this mutability and this perisha- 
bility exist for the materialist only. Newton's law, like 
Ptolemy's cycles, may in time pass completely out of prac- 
tical use, may cease to be a part of the active machinery of 
science; but Newton's law and Ptolemy's epicycles will 
surely, both alike, endure for evermore as works of art. 



16 



COLUMBIA UNIVERSITY PRESS 



A SERIES of twenty-two lectures descriptive in untechnical language of 
the achievements in Science, Philosophy and Art, and indicating the 
present status of these subjects as concepts of human knowledge, are being 
delivered at Columbia University, during the academic year 1907-1908, by 
various professors chosen to represent the several departments of instruction. 



MATHEMATICS, by Cassius Jackson Keyser, Adrain Professor of Mathe- 
matics. 
^PHYSICS, by Ernest Fox Nichols, Professor of Experimental Physics. 
t CHEMISTRY, by Charles F. Chandler, Professor of Chemistry. 
- ASTRONOMY, by Harold Jacoby, Rutherfurd Professor of Astronomy. 
GEOLOGY, by James Furman Kemp, Professor of Geology. 
BIOLOGY, by Edmund B. Wilson, Professor of Zoology. 
^ PHYSIOLOGY, by Frederic S. Lee, Professor of Physiology. 
■BOTANY, by Herbert Maule Richards, Professor of Botany. 

ZOOLOGY, by Henry E. Crampton, Professor of Zoology. 
^- ANTHROPOLOGY, by Franz Boas, Professor of Anthropology. 
•'■ARCHAEOLOGY, by James Rignall \Yhtt\tv, Professor of Greek Archae- 
ology and Art. 
HISTORY, by James Harvey Robinson, Professor of History. 
ECONOMICS, by Henry Rogers Seager, Professor of Political Economy. 
POLITICS, by Charles A. Beard, Adjunct Professor of Politics. 
JURISPRUDENCE, by Munroe Smith, Professor of Roman Law and 

Comparative Jurisprudence. 
SOCIOLOGY, by Franklin Henry Giddings, Professor of Sociology. 
PHILOSOPHY, by Nicholas Murray Butler, President of the University. 
PSYCHOLOGY, by Robert S. Woodworth, Adjunct Professor of Psy- 
chology. 
METAPHYSICS, by Frederick J. E. Woodbridge, Johnsonian Professor of 

Philosophy. 
ETHICS, by John Dewey, Professor of Philosophy. 

PHILOLOGY, by A. V. W. Jackson, Professor of Indo-Iranian Lan- 
guages. 
LITERATURE, by Harry Thurston Peck, Anthon Professor of the Latin 
Language and Literature. 



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